For stick on eyes my preference is to mount them on plastic.
Get a clear plastic lid or cut out some strips from a water bottle or something like this, just make sure to use clear plastic, not tinted or translucent (although tinted can produce some cool results).
Cut a teardrop shaped piece with the wide "bulb" of the teardrop about the diameter of the stick on eye. Scuff that end of the plastic a bit, I like a swipe with a small piece of sandpaper, and attach the eye to the plastic. A drop of superglue makes a much better bond than the stickie back. Then tie the other small tapered end of the plastic strip down at the head of the fly. To get the eye further back in the fly, just lengthen the tear drop and cut to fit.